Which of the following numbers is a multiple of 9? ${45,48,76,82,107}$
Explanation: The multiples of $9$ are $9$ $18$ $27$ $36$ ..... In general, any number that leaves no remainder when divided by $9$ is considered a multiple of $9$ We can start by dividing each of our answer choices by $9$ $45 \div 9 = 5$ $48 \div 9 = 5\text{ R }3$ $76 \div 9 = 8\text{ R }4$ $82 \div 9 = 9\text{ R }1$ $107 \div 9 = 11\text{ R }8$ The only answer choice that leaves no remainder after the division is $45$ $ 5$ $9$ $45$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $9$ are contained within the prime factors of $45$ $45 = 3\times3\times5 9 = 3\times3$ Therefore the only multiple of $9$ out of our choices is $45$. We can say that $45$ is divisible by $9$.